Abstract:
We consider algebraic groups defined over a field k and containing a maximal torus T which is defined and anisotropic over k and split over a given quadratic extension K of k. We study certain structural features of such groups, and the results obtained are used to investigate the behavior of these groups over special fields.
\Bibitem{Wei71}
\by B.~Yu.~Weisfeiler
\paper Semisimple algebraic groups which are split over a~quadratic extension
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 1
\pages 57--72
\mathnet{http://mi.mathnet.ru/eng/im1913}
\crossref{https://doi.org/10.1070/IM1971v005n01ABEH001007}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=277537}
\zmath{https://zbmath.org/?q=an:0237.20038}
Linking options:
https://www.mathnet.ru/eng/im1913
https://doi.org/10.1070/IM1971v005n01ABEH001007
https://www.mathnet.ru/eng/im/v35/i1/p56
This publication is cited in the following 4 articles:
Vladimir I. Chernousov, Andrei S. Rapinchuk, Igor A. Rapinchuk, “Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction”, Advances in Mathematics, 438 (2024), 109437
Nguyeñ Quôć ThĂńg, “Some local-global principles in the arithmetic of algebraic groups over real function fields”, Math Z, 221:1 (1996), 1
Gopal Prasad, Andrei S. Rapinchuk, “Computation of the metaplectic kernel”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 84:1 (1996), 91
B. Yu. Weisfeiler, “The Hasse principle for algebraic groups split over a quadratic extension”, Funct. Anal. Appl., 6:2 (1972), 102–104
Citation in format AMSBIB
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